Question:
The least number by which 72 be divided to make it a perfect cube, is________
Solution:
9
Resolving 72 into prime factors, we get
72=2 x 2 x 2 x 3 x 3
Grouping the factors in triplets of equal factors, we get
72 = (2 x 2 x 2) x 3 x 3
Clearly, if we divide 72 by 3 x 3, the quotient would be 2 x 2 x 2, which is a perfect cube. Hence, the least number by which 72 be divided to make
it, a perfect cube, is 9.